Originally Posted by

**s_ingram** Sorry if I have not been clear. I think we are in agreement actually. I am talking about the left hand side (LHS) and the right hand side of the equation $z^n - z^{-n} = i 2\sin t$

this should balance for any z, so if we take 1 + i then LHS = $\frac{1}{2} + i \frac{3}{2}$ for n = 1.

On the RHS we would have $i 2 \sin t$ and $t = \frac{\pi}{4}$ for z = 1 + i. i.e. $i \sqrt{2} $ so the LHS does not equal the RHS.

I was just trying to confirm that this is what you meant and that I hadn't made an error in my calculation.